X-Tel Corporation's dividends in year 1 and 2 are expected to be $3 and $4 respectively. Year 2's stock price is expected to be $40 per share. If the investor's return is 10%, determine the stock price now.
A) $39.09
B) $39.92
C) $40.35
D) $40.98
E) $41.46

Question

Quizplus · Accepted Answer

To find the current stock price, we use the dividend discount model for a multi-stage dividend. The formula to calculate the present value of the expected dividends and stock price is:$$ P_0 = \frac{D_1}{(1+r)^1} + \frac{D_2 + P_2}{(1+r)^2} $$Where:- $P_0$ is the current stock price,- $D_1$ and $D_2$ are the dividends in year 1 and 2 respectively,- $P_2$ is the stock price in year 2,- $r$ is the required rate of return (10% or 0.10 in decimal form).Plugging in the given values:$$ P_0 = \frac{3}{(1+0.10)^1} + \frac{4 + 40}{(1+0.10)^2} $$$$ P_0 = \frac{3}{1.10} + \frac{44}{1.21} $$$$ P_0 = 2.727 + 36.364 $$$$ P_0 = 39.091 $$Rounded to two decimal places, the current stock price is $39.09.

X-Tel Corporation's Dividends in Year 1 and 2 Are Expected